The mixture distribution models for interoccurence times of earthquakes

Abstract

Risk analyses made in the area of seismic activity are going to be of great importance in determining the earthquake interoccurence times. Several statistical methods have been developed for this purpose. Recently, Exponential, Gamma and Weibull distributions are the frequently used methods in this regard. In this study, we investigate the interoccurence time statistics of earthquakes which occurred in the area coordinated 39º–42º N latitude and 30º–40º E longitude in the North Anatolian Fault Zone (NAFZ) between the years 1960–2008, with a mixture of two different distributions of Exponential, Gamma and Weibull and a mixture of the same kind of distribution. We found that the mixture distributions are more suitable than the other examined distribution models for small magnitudes (mc ≥ 3). Also Weibull-Gamma and Weibull-Exponential distributions are agreeable for large magnitudes (mc ≥ 5).

A matrix-variate dirichlet process to model earthquake hypocentre temporal patterns

“…To our knowledge, other than these two bodies of work, no others have aimed to cluster the NMSZ from a purely statistical perspective. It should be pointed out that in a more general sense, numerous statistical clustering approaches including Kmeans/Kmedian (Kamat and Kamath, 2017;Novianti et al, 2017;Kuyuk et al, 2012;Ramdani et al, 2015;Malyshev, 2016), mixture models (Rhoades and Gerstenberger, 2009;Erisoglu et al, 2011;Rhoades, 2013;Kuyuk et al, 2012)) and spatial point processes (Veen and Schoenberg, 2006;Ogata, 1998;Schoenberg, 2003;Bray and Schoenberg, 2013) have been applied to earthquake data, but not the NMSZ data specifically. Thus, this work was motivated by a desire to statistically identify temporal patterns among earthquake occurrences within the NMSZ.…”

“…(2012); Ramdani et al. (2015); Malyshev (2016)), mixture models (Rhoades and Gerstenberger (2009); Erisoglu et al. (2011); Rhoades (2013); Kuyuk et al.…”